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Answer :
To determine which of the given proportions is false, let's go through each pair and check if the fractions are equivalent. Two fractions are equivalent if their cross products are equal.
Let's check each proportion:
1. Proportion 1:
[tex]\(\frac{12}{15} = \frac{20}{25}\)[/tex]
Cross-multiply:
- [tex]\(12 \times 25 = 300\)[/tex]
- [tex]\(15 \times 20 = 300\)[/tex]
Since both products are equal, this proportion is true.
2. Proportion 2:
[tex]\(\frac{20}{50} = \frac{40}{100}\)[/tex]
Cross-multiply:
- [tex]\(20 \times 100 = 2000\)[/tex]
- [tex]\(50 \times 40 = 2000\)[/tex]
Since both products are equal, this proportion is true.
3. Proportion 3:
[tex]\(\frac{25}{45} = \frac{50}{90}\)[/tex]
Cross-multiply:
- [tex]\(25 \times 90 = 2250\)[/tex]
- [tex]\(45 \times 50 = 2250\)[/tex]
Since both products are equal, this proportion is true.
4. Proportion 4:
[tex]\(\frac{18}{48} = \frac{30}{50}\)[/tex]
Cross-multiply:
- [tex]\(18 \times 50 = 900\)[/tex]
- [tex]\(48 \times 30 = 1440\)[/tex]
Since the products are not equal, this proportion is false.
Therefore, the false proportion is [tex]\(\frac{18}{48} = \frac{30}{50}\)[/tex]. This is the one that doesn't hold true.
Let's check each proportion:
1. Proportion 1:
[tex]\(\frac{12}{15} = \frac{20}{25}\)[/tex]
Cross-multiply:
- [tex]\(12 \times 25 = 300\)[/tex]
- [tex]\(15 \times 20 = 300\)[/tex]
Since both products are equal, this proportion is true.
2. Proportion 2:
[tex]\(\frac{20}{50} = \frac{40}{100}\)[/tex]
Cross-multiply:
- [tex]\(20 \times 100 = 2000\)[/tex]
- [tex]\(50 \times 40 = 2000\)[/tex]
Since both products are equal, this proportion is true.
3. Proportion 3:
[tex]\(\frac{25}{45} = \frac{50}{90}\)[/tex]
Cross-multiply:
- [tex]\(25 \times 90 = 2250\)[/tex]
- [tex]\(45 \times 50 = 2250\)[/tex]
Since both products are equal, this proportion is true.
4. Proportion 4:
[tex]\(\frac{18}{48} = \frac{30}{50}\)[/tex]
Cross-multiply:
- [tex]\(18 \times 50 = 900\)[/tex]
- [tex]\(48 \times 30 = 1440\)[/tex]
Since the products are not equal, this proportion is false.
Therefore, the false proportion is [tex]\(\frac{18}{48} = \frac{30}{50}\)[/tex]. This is the one that doesn't hold true.
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